Simple array of two antennas
Consider two identical parallel Hertzian dipoles separated by a distance d
The dipole currents have the same amplitude and total phase difference
The electric far-field components at the observation point are
At long distance
Chapter IV
Linear antennas
Theory of Linear Dipole Antenna Arrays of Linear Dipole Antennas
Antennas
Antennas are transducers that transfer electromagnetic energy between a transmission line and free space.
From a circuit point of view, a transmitting ant
Waveguide Cavity Resonator
The cavity resonator is obtained from a section of rectangular wave guide, closed by two additional metal plates. We assume again perfectly conducting walls and loss-less dielectric.
The addition of a new set of plates introduce
Assume perfectly conducting walls and perfect dielectric filling the wave guide. Convention : a is always the wider side of the wave guide.
It is useful to consider the parallel plate wave guide as a starting point. The rectangular wave guide has the same
Dielectric Wave Guide
A dielectric waveguide is a structure which exploits total reflection at dielectric interfaces to guide electromagnetic radiation. The simplest case is the symmetric dielectric slab wave guide
For guidance one must have
Similarly to
Oblique incidence: Interface between dielectric media
Consider a planar interface between two dielectric media. A plane wave is incident at an angle from medium 1. The interface plane defines the boundary between the media. The plane of incidence contains
Parallel Plate Waveguide
Maxwell's equations
Wave equation for Transverse Electric (TE) modes
From (4) & (6) & (2)
Wave equation for Transverse Magnetic (TM) modes
Transverse Electric (TE) modes
This solution satisfies the boundary conditions:
We have
and
Incidence on Perfect Conductor
Consider first normal incidence at an interface between a dielectric and a perfect conductor. Total reflection occurs, as in a shortcircuited transmission line.
Because of interference between incident and reflected wave, th
For a uniform plane wave with general orientation, the direction of propagation is identified by the propagation vector, normal to the phase planes
Considering the position vector
we have the scalar dot product
Plane Waves in Arbitrary Directions
Source i
Normal Incidence on an Interface
Consider a planar interface between two unbounded media, and a uniform plane wave with normal incidence on the interface.
Because of the medium discontinuity, the incident wave experiences a partial reflection at the inter
Power Flow in Electromagnetic Waves
The time-dependent power flow density of an electromagnetic wave is given by the instantaneous Poynting vector
For time-varying fields it is important to consider the time-average power flow density
where T is the perio
Electromagnetic Waves in Material Media
In a material medium free charges may be present, which generate a current under the influence of the wave electric field. The current Jc is related to the electric field E through the conductivity as
The material m
Doppler Effect
An observer moves along the direction of propagation of the electromagnetic wave, with constant velocity vo . Because of its movement, the observer will detect phase planes of the wave at a different rate than in stationary position, as
The
Review of Boundary Conditions
Consider an electromagnetic field at the boundary between two materials with different properties. The tangent and the normal component of the fields must me examined separately, in order to understand the effects of the boun
Electromagnetic Waves
For fast-varying phenomena, the displacement current cannot be neglected, and the full set of Maxwell's equations must be used
The two curl equations are analogous to the coupled (first order) equations for voltage and current used i
Review: Time Varying Fields
In the dynamics case, we can distinguish between two regimes:
Low Frequency (Slowly-Varying Fields) The displacement
current is negligible in the Maxwell's equations, since
High Frequency (Fast-Varying Fields) The general set o
Review: Electrostatics and Magnetostatics
In the static regime, electromagnetic quantities do not vary as a function of time. We have two main cases: ELECTROSTATICS The electric charges do not change position in time. Therefore, , E and D are constant and
Chapter III Electromagnetic Waves
Maxwell's Equations Electrostatics and Magnetostatics Time Varying Fields Electromagnetic Plane Waves Boundary Conditions Doppler Effect Electromagnetic Waves In Material Media Power Flow Normal Incidence On An Interface
There are two design parameters for double stub matching: The length of the first stub line Lstub1 The length of the second stub line Lstub2
In the double stub configuration, the stubs are inserted at predetermined locations. In this way, if the load impe
There are two design parameters for single stub matching:
The location of the stub with reference to the load dstub The length of the stub line Lstub
Any load impedance can be matched to the line by using single stub technique. The drawback of this appro
Impedance Matching
A number of techniques can be used to eliminate reflections when line characteristic impedance and load impedance are mismatched. Impedance matching techniques can be designed to be effective for a specific frequency of operation (narro
Smith Chart
The Smith chart is one of the most useful graphical tools for high frequency circuit applications. The chart provides a clever way to visualize complex functions and it continues to endure popularity decades after its original conception. From
Standing Wave Patterns
In practical applications it is very convenient to plot the magnitude of phasor voltage and phasor current along the transmission line. These are the standing wave patterns:
The standing wave patterns provide the top envelopes that
Transient and Steady-State on a Transmission Line
We need to give now a physical interpretation of the mathematical results obtained for transmission lines. First of all, note that we are considering a steady-state regime where the wave propagation along
We have obtained the following solutions for the steady-state voltage and current phasors in a transmission line:
Loss-less line
Lossy line
V ( z ) = V + e- j z + V - e j z V ( z ) = V + e - z + V - e z 1 + - j z - j z 1 + - z I ( z ) = ( V e - V e ) I (
Chapter II
Transmission Lines
Transmission Line Equations Transmission Line Properties Discussion Of Steady State Regime Standing Wave Patterns And VSWR Introduction To Smith Chart Impedance Matching 1 Impedance Matching 2 Impedance Matching 3
1
Transmiss
Power in Circuits
Consider the input impedance of a transmission line circuit, with an applied voltage v(t) inducing an input current i(t).
For sinusoidal excitation, we can write
v(t ) = V0 cos(t ) i (t ) = I 0 cos(t - )
- / 2, / 2 ] [
where is the phas
Chapter I Circuits
Complex numbers, Phasors, and Circuits Power in Circuits
1
Complex Numbers, Phasors and Circuits
Complex numbers are defined by points or vectors in the complex plane, and can be represented in Cartesian coordinates
z = a + jb
or in po